Question

G and H are mutually exclusive events. P(G)=0.5 P(H)=0.3. a. Explain why the following statement MUST be false: P(H|G)=0.4. b. Find P(H OR G). c. Are G and H independent or dependent events? Explain in a complete sentence.

Answer #1

**Solution:**

We are given that: G and H are mutually exclusive events.

Thus

and we are also given that: P(G)=0.5 P(H)=0.3.

**Part a) Explain why the following statement MUST be
false: P(H|G)=0.4.**

Since , P( H | G) becomes 0.

Hence given statement P(H|G)=0.4 must be false.

**Part b) Find P(H** **OR
G****).**

Since G and H are mutually exlcusive events,

P( H or G) = P(H) + P(G)

P( H or G) = 0.3 + 0.5

P( H or G) = 0.8

**Part c) Are G and H independent or dependent
events?**

Events are independent if and only if:

We have

and

P(G) X P(H) = 0.5 X 0.3

P(G) X P(H) = 0.15

Thus we get:

Hence events G and H are not independent,

**that is: events G and H are dependent
events.**

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0.8.
Find P(A and B)
2. Suppose that P(A) = 0.3, P(B) = 0.4, and
P(A and B) = 0.12.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent
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are
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known to be mutually exclusive
b. Two events cannot be...

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P(B) = 0.8, and P(A) =
0.5
P(A | B) = 0.3,
P(B) = 0.8, and P(A) =
0.3
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(b) Assume A and B are mutually exclusive
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